Circular Rainbow (with plane inside)

So...here is my once-in-a-lifetime event. My wife and I were flying to Miami a little while ago and happened to look out the window to see this amazing circular rainbow. Now, I know "all" rainbows are in fact circular, but given that 99% of us see them from the ground, it almost never looks that way.

Then it didn't end there. While we were mesmerized by the rainbow itself, as we watched, things got even more amazing when we noticed the shadow of our plane *inside* the rainbow.

Absolutely amazing. Has anyone ever seen this phenomenon?

Full disclosure...other than adding a little contrast via Picassa, I have made no changes to these photos. And if you want to know more about circular rainbows...check out this link: http://www.wonderquest.com/rainbow-circle.htm